Photo credit of Otzi: South Tyrol Museum of Archaeology/EURAC/Samadelli/Staschitz).

Very exciting news on the tattoo history front: the oldest tattoos known to date do, indeed, belong to "Otzi the Iceman," whose frozen mummified body, with a total of 61 tattoos, was found accidentally, in 1991, by two hikers in the Otztal Alps along the Austrian-Italian border. It is estimated that Otzi died between about 3370 and 3100 BC, and so many deemed him to be the OG of tattooed mummies; however, there was debate among tattoo scholars that Otzi may not have been, and instead, the title could belong to an unidentified South American Chinchorro mummy who was found with a tattooed "mustache." There were a number of questions surrounding the identify and age of that mummy, and so to put the debate to rest, scholars Aaron Deter-Wolf, Lars Krutak, Benoit Robitaille, and Sebastien Galliot collaborated to uncover the identity of the Chinchorro specimen. And they did. But they didn't just stop there. They also compiled a reference list of tattooed mummies from across
the globe, demonstrating that Otzi wears the oldest
tattoos identified to date.

Before officially declaring Otzi to be the
oldest tattooed individual, we double checked our data by compiling a
list of tattooed human mummies from around the globe. This catalog
included at least 49 sites spanning the period between around 3370 BC
and AD 1600, and spread throughout the American Arctic, Siberia,
Mongolia, western China, Egypt, Sudan, the Philippines, and Greenland in
addition to Europe and South America. Some of these finds, such as the Princess of Ukok, the men and women from Burials 2 and 5 at the Pazyryk burial ground, and the woman from Grave 50 at 3-J-23, et-Tereif, Sudan
have been well-publicized outside of academia. Others are mentioned
simply in passing in early archaeological reports, or appear only in
regional and hard-to access journals. A number of sites include multiple
tattooed individuals, sometimes numbering in the dozens. In all we were
able to identify eleven tattooed mummies greater than 4,000 years old
(about 2000 BC). In addition to Ötzi and the Chinchorro man these
include seven individuals from Egypt, and two from Russia. To date, Otzi
is the oldest of these finds.

As noted in the journal, while Otzi is the oldest of the finds, it is unlikely that he's the first tattooed person on earth. The report explains:

[...] Otzi's 61 marks represent physical actions performed on his body as part of established social or therapeutic practices that almost certainly existed within his culture well
before his birth. While other lines of archeological evidence hint that
permanent body marking may extend significantly earlier into human
history [...] conclusive proof of the antiquity of tattooing
has yet to be uncovered. We anticipate that future research including
new archeological
finds, reanalysis of existing collections, advanced dating techniques, and the application of new imaging technologies in the
study of mummified human remains will provide additional data
through which to further evaluate this ancient and global practice, and
likely provide direct evidence of tattooing antedating 3200 BC.

I highly recommend reading the report. In addition to their findings and tattooed mummy table, there are some great links and references to further reading.